Break up an integer into all possible groups without changing the order in which the digits are arranged, then multiply each set of groups out and sum the products.
Example: 326. 3x2x6, + 32x6, + 3x26 gives 36 + 192 + 78 = 306. If the result equals the original integer, it's an Ellis number.
How many Ellis numbers are there in the integers up to 10,000?
Sometimes the process leads to an integer which isn't an Ellis number but which, when subjected to the same process, leads back to the original number, and is thus a sort of cyclic Ellis number. Find all cyclic Ellis numbers less than 10,000.